We have carried out submillimeter 12CO(J = 3-2) observations of six giant molecular clouds (GMCs) in the Large Magellanic Cloud (LMC) with the ASTE 10 m submillimeter telescope at a spatial resolution of 5 pc and very high sensitivity. We have identified 32 molecular clumps in the GMCs and revealed significant details of the warm and dense molecular gas with n(H2) ~ 103-105 cm-3 and Tkin ~ 60 K. These data are combined with 12CO(J = 1-0) and 13CO(J = 1-0) results and compared with LVG calculations, The results indicate that clumps that we detected are distributed continuously from cool (~10-30 K) to warm (≥ 30-200 K), and warm clumps are distributed from less dense (~103 cm-3) to dense (~1035-10 5 cm-3). We found that the ratio of 12CO(J = 3-2) to 12CO(J = 1-0) emission is sensitive to and is well correlated with the local Hα flux. We infer that differences of clump properties represent an evolutionary sequence of GMCs in terms of density increase leading to star formation. Type I and II GMCs (starless GMCs and GMCs with H ii regions only, respectively) are at the young phase of star formation where density does not yet become high enough to show active star formation, and Type III GMCs (GMCs with H ii regions and young star clusters) represent the later phase where the average density is increased and the GMCs are forming massive stars. The high kinetic temperature correlated with Hα flux suggests that FUV heating is dominant in the molecular gas of the LMC.